Mathematical and numerical analysis of the dynamical behavior of chen oscillator

Over the years, chaos has been an important subject of interest to many researchers. Many chaotic oscillators have been proposed in literature. The oscillating and the possible stability in chaotic systems could be applied as fundamental tools in developing real world applications in several disciplines such as engineering, telecommunication, medicine, etc. In this work, the Chen oscillator dynamic and stability behavior are studied by applying mathematical and numerical analyses to investigate the equilibria, eigenvalues, Lyapunov exponents and bifurcation diagrams. The eigenvalues obtained show that the Chen oscillator is unstable at the equilibrium points examined while the maximum Lyapunov exponent obtained confirms its chaotic nature. Also, the bifurcation diagrams show the stability of the Chen system with the three system parameters. The results show that bifurcation with parameter b gives the longest period of stability.